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US 2010/0250475 A1Published application
Tensor voting in N dimensional spaces
AssigneeUniversity of Southern California
InventorsGerard Medioni, Philippos Mordohai
Life of this patent
Estimating the term…
Abstract
A tensor voting scheme which can be used in an arbitrary number N of dimensions, up to several hundreds. The voting scheme can operate on unorganized point inputs, which can be oriented or unoriented, and estimate the intrinsic dimensionality at each point. Moreover it can estimate the tangent and normal space of a manifold passing through each point based solely on local operations.
Claims37
A method performed by an apparatus comprising:
- receiving as input a plurality of points in an N-dimensional space, where N can be any number between 2 and 500;
- defining the received plurality of points as second order, symmetric, nonnegative definite tensors that encode an orientation and confidence of the orientation of each point based on known prior orientation information;
- voting between points to determine, in an unsupervised manner, at least one likely D-dimensional manifold on which said points lie, where D is less than or equal to N, wherein said voting propagates the orientation information and the confidence of the orientation among the plurality of input points that are encoded as different types of tensors comprising stick and ball tensors based on the known prior orientation information, wherein the voting is performed independent of voting fields and without storing the voting fields;
- and
- producing and outputting information about said at least one D-dimensional manifold used to find relations between points that cannot be visualized in at least one of pattern recognition, data mining, kinematics, non-linear interpolation and visualization.
2 more elements
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An apparatus comprising:
- a storage unit, storing information about a plurality of points in an N-dimensional space, wherein N is any number between 2 and 500, as second order, symmetric, nonnegative definite tensors that encode an orientation and confidence of the orientation of each point based on known prior orientation information;
- and
- a processor, carrying out a voting between said points to determine, in an unsupervised manner, at least one likely D-dimensional manifold on which said points lie, where D is less than or equal to N wherein said voting propagates the orientation information and the confidence of the orientation among the plurality of input points that are encoded as different types of tensors comprising stick and ball tensors based on the known prior orientation information, wherein the voting is performed independent of voting fields and without storing the voting fields to form information about said at least one D dimensional manifold.
An apparatus comprising:
- a storage unit, storing information about a plurality of points in an N-dimensional space, wherein N is any number between 2 and 500, according to a tensor representation that encodes an orientation information and confidence of the orientation for each point based on known prior orientation information;
- and
- a processor forming, transmitting and analyzing votes from each of the plurality of points to another point in an unsupervised manner independent of voting fields and without storing the voting fields by encoding each point as different types of tensors comprising stick and ball tensors based on the known prior orientation information, said votes representing information about at least one D dimensional manifold on which the points lie, wherein D is less than or equal to N, and producing and outputting information about said at least one D dimensional manifold, based on said forming and analyzing.
(canceled)
An apparatus comprising:
- a computer comprising:
- a memory that stores a definition of a plurality of points in an N-dimensional space, wherein N is any number between 2 and 500, according to a tensor representation that encodes orientation information for each point and confidence of the orientation of each point based on known prior orientation information;
- and
- a processor that forms and analyzes votes from each of the plurality of points to another point in an unsupervised manner, said votes representing information about at least one D dimensional manifold on which the points lie, wherein D is less than or equal to N and wherein the votes are formed independent of voting fields and without storing the voting fields by encoding each point as different types of tensors comprising stick and ball tensors based on the known prior orientation information, and producing information about said at least one D dimensional manifold;
- wherein the processor is configured to form and analyze the votes by estimating an arc between a voter point and a receiver point having an arc length, S, calculated based on the following:
- S
-
- (
- s
- ,
- l
- ,
- θ
- )
- =
-
- -
- (
- s
- 2
- +
- cK
- 2
- σ
- 2
- )
- [
- -
- sin
-
- (
- 2
-
- θ
- )
- cos
-
- (
- 2
-
- θ
- )
- ]
-
- [
- -
- sin
-
- (
- 2
-
-
- θ
- )
-
- cos
-
- (
- 2
-
- θ
- )
- ]
- s
- =
- θ
-
-
-
- v
- ->
-
- sin
-
- (
- θ
- )
- ,
- K
- =
- 2
-
- sin
-
- (
- θ
- )
-
- v
- ->
-
- ,
- wherein K represents a curvature of the arc, σ represents a scale of voting, c is a constant, θ represents an angle of the arc, and {right arrow over (v)} represents a vector connection between the voting and the receiving points.
90 more elements
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Dependencies are inferred from the claim text.